nshivapu wrote:
If \(n\) is a positive integer, is \(n^x\) an even number?
(1) \(n\) is an even number. If \(x=0\) then \(n^x=1=\text{odd}\) but if \(x=1\) then \(n^x=n=\text{even}\). Not sufficient.
(2) \(x^2-3x+2 = 0\). Either \(x=1\) or \(x=2\). Not sufficient, since no info about \(n\).
(1)+(2) Since given that \(n=\text{even}\) then both \(n^1\) and \(n^2\) will be even. Sufficient.
Answer: C
It is given that (in the question stem) n is a positive integer, that means n>0
Now, if S1 specifies that, n is also even, that means n>1
Thus, eg: 2^x where x irrespective of being odd or even is still going to leave n^x as even
On solving S2 we get S as either 1 or 2. Thus, insufficient
And, I arrived at answer as A
Kindly let me know how do I guard against such ambiguity, of what is specified in the question stem vs the Statements. I mean should I consider statements independent of the question stems or Should question stems stand as true come what may.
Thanks, Pls correct me if I am wrong.
On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. _________________
In this question notice that the stem says that n is a positive integer and then (1) says that it's even, so n could be 2, 4, 6, 8, ... Notice also, that neither the stem nor the first statement says anything about x. It could be even or odd, it could be a fraction, or an irrational number.
If x is a positive integer, then n^x = (positive even integer)^(positive integer) = even. But if say x is a fraction, then n^x won't necessarily be even, for example, if n = 2 and x = 1/2, then \(n^x=\sqrt{2}\), which is not an integer, hence is not even. Or consider example given in the solution: \(x=0\) then \(n^x=1=\text{odd}\). So, from (1) n^x could be even, odd or not an integer at all, which means that (1) is NOT sufficient.
Does this make sense?
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